In a projection optical lithography system, a template of the desired circuit patterns is inscribed onto a 4-times (4×) enlarged reticle or photo-mask, which is then repeatedly illuminated with monochromatic actinic light, and the diffracted light imaged through a sophisticated optical system, and focused into a layer of light-sensitive photo-resist coated onto the surface of a silicon wafer. In optical lithography for microchip manufacturing, it is important that the focal ranges of all patterns in the layout be centered quite closely on a common plane in order to achieve a maximum common process window, since positioning errors and wafer non-flatness leave little focus margin with which to absorb shifts in the focused position of individual feature images. It is desirable, then, that all layout patterns be simultaneously in good focus within a plane at the midpoint of their focal ranges, and that this plane be common to all features. The focal range midpoint for a particular feature is referred to as the plane of best focus for that feature, and it is desirable that the best-focus planes of all patterns in the layout coincide with one another as closely as possible.
At present, very aggressive lithographic methods to print semiconductor technology nodes down to 10 nm using ultraviolet light of 193 nm wavelength are driving very small mask and wafer dimensions, as well as very tight process control requirements. At such a scale, variability specifications for focus, dose, overlay, and other factors are in the nanometer range for the most critical levels. For instance, the acceptable common depth of focus, measured as the range of focus over which every circuit pattern successfully prints within specs, for some of the most critical levels in typical 22 nm technology nodes, is of the order of 90 nm, becoming even tighter for 14 nm and 10 nm technology.
Relatively large shifts in the position of best focus have been observed on wafer for grating patterns of varying pitch and pattern type. These focus shifts can be traced back to phase errors induced by the transmission through subwavelength openings in the mask topography in the interfering beams that form the image intensity fringes at the wafer plane. In other words, the electromagnetic field scattering on the topography of the mask finite thickness results in changes in the phase of the diffracted orders, and these phase changes translate into shifts in the plane of best focus observed on wafer. These phase shifts are different for different mask patterns and can be responsible for shifts in focus that are as large as 60 nm in binary mask blanks commonly employed in lithography [Ref: J. Tirapu-Azpiroz, G. W. Burr, A. E. Rosenbluth, and M. Hibbs. “Massively-parallel FDTD simulations to address mask electromagnetic effects in hyper-NA immersion lithography.” Proc. SPIE 6924, 69240Y (2008)]. In particular, large shifts in positions of best focus have been observed between very dense pitches and more isolated features. The distortions in the transmitted electromagnetic field that the topography of finite-thickness masks introduces are generally referred to as “EMF effects”.
When circuit features on masks are large compared to the exposing wavelength, it can be convenient to approximate the mask as an ideally thin diffracting screen. This standard approximation is referred to as the Thin Mask Approximation (TMA). However, even on the 4× enlarged masks that are typically used, circuit features today can be narrower than the exposing wavelength, and the mask design must take into account the fact that the patterns delineated on realistic masks will occupy an appreciable thickness along the optical axis, corresponding, for example, to the thickness of a patterned opaque mask film, with this topographical thickness of the patterns being almost comparable to their width in some cases. Because of the finite-thickness topography, physical masks do not behave precisely like ideal diffracting screens, and, in particular, the phase of the light that diffracts into different orders can be shifted.
Lithographic lenses converge the collected diffracted light to an image that ideally will be focused at the wafer. The curvature component of the directional variation in the phase of the light that converges to a particular printed feature on the wafer from different directions within the lens exit aperture defines the best-focus position of the feature. This curvature component is essentially the quadratic phase component of the converging directional distribution. The resolution of lithographic lenses is nowadays comparable to the separation between adjacent printed features, and the resolution functions of lenses also have long “tails” that extend quite far from the geometrical image point, so the distribution of light and associated phase that converges to any particular wafer feature will typically be influenced by the topography-induced phase shifts from all other features within an extended neighborhood surrounding the particular feature. This kind of finite-range dependence is customarily referred to as an optical proximity effect, and the range over which optical proximity effects between neighboring features are considered important is often referred to as an ambit, or as an optical diameter. Typical optical diameters are in the range of about 1 micron to 2 microns.
Overall, while these topography effects show a complex dependency on the mask and illumination characteristics, they can be understood in terms of deviations in the amplitude and phase of the diffracted fields as compared to those predicted by the thin mask approximation (TMA). Transmission losses in the mask beyond the TMA prediction are responsible for amplitude errors in the aerial image intensity, and can often be approximated with a simple bias applied to the mask edge to decrease the aperture size. Phase errors, on the other hand, tend to shift the position of best focus as explained above, and are difficult to correct with a simple uniform mask bias. In the idealized TMA model, the phase difference between diffracted orders from the mask that reach the wafer to form the aerial image is exactly zero or 180 degrees (neglecting pattern asymmetries for simplicity); hence this phase difference, as well as the aerial image field amplitude, is always a real valued number with no imaginary or quadrature component. In a realistic photomask with a finite thickness, the diffracted order fields emerging from the mask will experience different amounts of phase shift, and the relative phase difference between orders can be any value between 0 and 360 degrees. Similarly, the field amplitude of the aerial image produced by the interference of those diffracted orders will no longer be purely real valued, and will contain an imaginary or quadrature component responsible for the pattern-dependent shifts in focus observed at the image space.
More generally, any physical mechanism that gives rise to pattern-dependent variations in the plane of best focus can be detrimental to good process performance. Such variations result from several physical effects, such as: 1) mask topography in small mask features; 2) lens aberrations, some of which may be caused by lens heating; and 3) thin-film interference effects occurring within the resist film stack.
Adjustments applied to the lens within the exposure tool can be made to compensate for the impact of lens aberrations in the projection pupil. In addition, compensation for focus variations due to mask topography through deliberate introduction of lens aberrations in the pupil has been proposed, but such exposure-tool compensation schemes would merely provide global-only blanket mitigation of mask EMF-effects, making it difficult to fine-tune the corrections on a pattern-by-pattern basis or to take pattern proximity into account. [Ref: F. Staals et al., “Advanced wavefront engineering for improved imaging and overlay applications on a 1.35 NA immersion scanner,” SPIE v. 7973 (2011): p. 79731G.]
Compensating for the undesired phase shifts induced by mask topography with new added features, known as Anti-Boundary Layers, on the mask has also been proposed. The Anti-Boundary-Layer method corrects EMF effects by adding a compensating phase-shifter strip along mask edges. In order to create the phase-shifter strip, the mask quartz is etched to a predetermined optimum depth and along a predetermined optimum width, both parameters requiring careful control in three dimensions.